Apparatus for reducing dissipation rate of fluid ejected into boundary layer

ABSTRACT

A method and apparatus for ejecting a second fluid into the near-wall region of the boundary layer of a first fluid, so that the second fluid hugs the wall. This alone reduces drag by modifying the behavior of the near-wall structure, thereby reducing the frequency of burst and sweep cycles, even when the first and second fluids are identical. Further, one or more additives, such as polymer, surfactant, micro-bubbles, a combination thereof, and/or using a second fluid having an elevated temperature as compared to the temperature of the first fluid, may be used to achieve much greater drag reduction as well as lower dissipation rates than previously possible. The second fluid is ejected using a convex Coanda surface ( 7 ) and at a controlled velocity that is a small fraction of the velocity of the first fluid moving along the wall so that the flow lines of the second fluid are substantially aligned with the flow lines of the first fluid. To make the second fluid continue to hug the wall after ejection, vortices are generated in the second fluid by a concave surface ( 2 ) so that low pressure regions exist at the wall.

BACKGROUND OF INVENTION

[0001] Injection of additives such as microbubbles or high molecularweight materials such as polymers into the boundary layer of a fluidflow has been shown to reduce skin friction drag significantly for bothvessels moving relative to water and for pipeline applications. Themicrobubbles or large polymer molecules interact with the turbulentactivity in the near-wall region, absorbing energy and reducing thefrequency of burst (high energy fluid moving away from the wall) andsweep (low energy fluid replacing the high energy fluid in the near-wallregion) cycles. The reduced burst frequency results in less energydissipation from the wall and can result in skin friction dragreductions up to 80%. Experiments have shown that the efficacy ofpolymer molecules for drag reduction is closely related to theirmolecular weight, their location in the boundary layer, and the degreeto which they have been unwound, aligned, and stretched (i.e.,“conditioned”).

[0002] In the past, polymer mixture ejectors have been simple slots thatejected a mixture/solution of polymer and a fluid at an angle to thewall. To attain high drag reduction for a reasonable distance downstreamwith this ejection approach, large quantities and high concentrations ofpolymers must be ejected in order to flood the entire boundary area,creating a “polymer ocean” effect in the boundary layer. The highpolymer consumption rates of these systems have made them impracticalfor many drag reduction applications.

[0003] Fluids containing other substances than high molecular weightmaterials, e.g. micro-bubbles, surfactant, etc., as well as fluids withor without additive which are heated so as to achieve a lower viscosityin the viscous sublayer, have been used in prior art attempts to reducesurface friction drag. These, however, each require very large amountsof additive or quantities of heated fluid. To be useful for practicalapplications, a more efficient method for ejecting additive(s) orfluids, such as low viscosity or heated fluids, for drag reduction needsto be devised.

[0004] Another method to reduce skin friction is to impose on thesurface narrow microgrooves, commonly referred to as riblets. Theriblets also affect the development of turbulent structures in thenear-wall region and thereby reduce the burst frequency. While thetechnique does not require the expenditure of consumables such aspolymers, the level of drag reduction is more modest than withadditives, usually about 6 to 12 percent. Further, such systems are noteffective for marine surfaces that are exposed to microfouling frombiological slimes. Since slimes begin to form in a matter of hours,riblets are only practical for marine surfaces that can be regularlycleaned. Thus, a technique to affect the development of turbulence whichdoes not require the expenditure of additives but which is tolerant ofthe marine environment also will be useful even if the effect is modestrelative to polymer drag reduction.

BRIEF SUMMARY OF THE INVENTION

[0005] The present invention enables the efficient ejection of fluidmixtures/solutions containing a drag-reducing additive or additives intothe near-wall region of a boundary layer of a fluid flow in order toreduce drag. A first object of the invention is to enable drag to bereduced for a first fluid moving relative to a surface by ejecting asecond fluid into the near-wall region of the boundary layer of thesurface such that the second fluid retards or inhibits the “burst” and“sweep” cycles, as discussed above. The second fluid may or may not: (1)be the same fluid as the first fluid, (2) be of lower viscosity (e.g.,elevated in temperature) relative to the first fluid, and/or (3) containone or more drag-reducing substances as an additive in mixture orsolution. A second object of the invention is to release a drag-reducingsubstance only into the near-wall region of the boundary layer, byejecting it substantially parallel with the streamlines of the boundarylayer. A third object of the invention is to extend the time thedrag-reducing substance is operative in the near-wall region of theboundary layer by creating low pressure regions immediately adjacent thewall. When a drag-reducing substance is added to the second fluid, thedrag-reducing substance may comprise a mixture/aqueous solution of highmolecular weight polymer, surfactant, gas micro-bubbles, or anycombination thereof When the additive includes polymer, a fourth objectof the invention is to condition the polymer molecules prior to ejectionso that drag reduction occurs almost immediately upon ejection into thefirst fluid.

[0006] When a drag-reducing additive that includes polymer is used, thepresent invention preconditions the drag reducing mixture/solution forimproved drag reduction performance using a unique arrangement of flowarea restrictions, as well as by employing dimples, grooves andelastomeric materials. The dimples, grooves and flow area restrictionsare sized relative to one another and to the Reynolds number of the flowfor optimal polymer molecule conditioning (unwinding, aligning with theflow and stretching) so as to provide optimal drag reduction afterejection into the fluid flow.

[0007] The present invention uses a new approach to ejecting the secondfluid so that it minimizes disruption of the boundary layer of the firstfluid. This aspect of the invention employs a convex Coanda surface onthe downstream side of a slot ejector and controls the ejected velocityso as to be a small fraction of the flow velocity of the first fluidpast the surface, thereby enabling the stream lines of the second fluidto be nearly parallel with the streamlines of the first fluid.

[0008] The present invention also uses a new approach to structuring theflow in order to reduce migration/dissipation of the second fluid awayfrom the near-wall region of the downstream wall. This is achieved byone or more ejectors, each having a carefully designed chamber under theslot. The upstream wall of the chamber has the surface curvature andfeatures that establish a duct-like system of longitudinal (i.e., in thedirection of the flow) Görtler vortices. Görtler vortices are formed bythe centrifugal effect of a fluid flow that is given angular velocity bya concave surface. The duct-like system of Gdrtler vortices formed bythe present invention mimic the spacing, but have the opposite rotation,of the naturally occurring quasi-longitudinal vortex pairs in theboundary layer. The pairing of naturally occurring quasi-longitudinalvortex pairs is such that they migrate from the wall and are believed tocontribute to the development of bursts and sweeps that account for alarge portion of hydrodynamic drag. The vortex pairs, created by theupstream wall of the chamber, have an inverted orientation relative tothe downstream wall and thus opposite signs of rotation that cause thevortex pairs to hug the downstream wall as they pass along it afterbeing shed from the chamber. This advantageously causes the second fluidor drag-reducing substance that has been ejected into the near-wallregion of the boundary layer of a first fluid flowing by the wall toremain in the near-wall region. It also enables drag reduction to beachieved (by reducing the frequency of burst and sweep cycles) when thesecond fluid contains no additives, is identical in temperature, and isthe same type fluid as the first fluid.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009] The present invention will become more fully understood from thedetailed description given below and the accompanying drawings, whichare given by way of illustration only and thus are not limitative of thepresent invention, wherein:

[0010]FIG. 1 depicts Görtler vortices forming due to centrifulgal forcescaused by drag on a concave surface,

[0011]FIGS. 2A illustrates, in isometric view, the formation process ofnaturally generated quasi-longitudinal vortex pairs which, as is wellknown in the art, evolve in the near-wall region of a turbulent boundarylayer.

[0012]FIG. 2B is a cross-sectional view of a fully developed, Görtlervortex pair adjacent a surface from which, as is well known in the art,occur in an unrestricted flow of a fluid over a concave surface or wherea cross-sectional area of a restricted flow temporarily increases in theregion of the concave surface, such as in a chamber, so as to allowpaired Görtler vortices to form;

[0013]FIG. 2C is a cross-sectional view of a fully developed, Görtlervortex pair which has been shed by an upstream surface of oppositeorientation and now is adjacent a downstream surface, and which rotatewith directions opposite to the naturally occurring vortex pairillustrated in FIG. 2B;

[0014]FIG. 3 depicts a side view of a vortex ejector used to practicethe method of the invention, with the lower portion thereof being across-sectional view which shows the inner components of the vortex ductejector,

[0015]FIG. 4 illustrates, in cross-sectional view, a cone component ofthe ejector shown in FIG. 3,

[0016]FIG. 5 illustrates, in cross-sectional view, a diffuser componentof the ejector shown in FIG. 3, and

[0017]FIG. 6 illustrates, in cross-sectional view, a portion of anejector ring.

DETAILED DESCRIPTION

[0018] The present invention achieves more effective and more efficientdrag-reducing substance mixture/solution ejection by releasing adrag-reducing substance mixture/solution into the near-wall region ofthe boundary layer and by controlling the characteristics of themixture/solution flow so that the mixture/solution becomes effectivemore quickly and remains for a longer period of time in the near-wallregion. By producing a mixture/solution with flow characteristics thatadhere it to the wall, the ejector extends the drag-reducing substanceresidence time in the near-wall region before it is diffused into thesurrounding fluid, and thus reduces additive consumption of a dragreduction system.

[0019] Görtler vortices are formed by the centrifugal effect of asubtantially “free” (meaning relatively unconstrained, unlike flow in apipe or duct of constant cross-section) flow that is given angularvelocity by a concave surface. FIG. 1 depicts naturally occurring,quasi-longitudinal Görtler vortices 1 forming due to centrifugal forcescaused by the flow 5 over a concave surface 2. The surface features ofthe ejector of the present invention create Görtler vortices that mimicthe spacing of the naturally occurring quasi-longitudinal vortex pairsin the boundary layer, but they are produced on the upstream wall andthus are inverted in orientation relative to the downstream wall. Thisoccurs due to the downstream wall surface normal being inverted relativeto the surface normal of the chamber wall where the vortices are shed.The pairing of naturally occurring quasi-longitudinal vortex pairs issuch that pressure differentials produced cause them to migrate from thewall at which they are formed and are believed to contribute to thedevelopment of bursts and sweeps that account for a large portion ofhydrodynamic drag.

[0020]FIG. 2A depicts a schematic view of quasi-longitudinal vortexpairs which are created in the near-wall region of turbulent flow. It isgenerally accepted that flow 5 over a stationary surface 4 createstransverse structures which become distorted into hairpin-shapedvortices 3 near the wall. The quasi-streamwise “legs” of eachhairpin-shaped vortex produce a pressure differential normal to the wallthat makes the vortex pair migrate away from the surface 4. FIG. 2(b) isa transverse cross-sectional schematic of such a vortex pair inducing apressure differential that will move it away from the wall. The “H”represents a local higher pressure region, and the “L” represents alocal lower pressure region. In contrast to a naturally occurring vortexpair, the Görtler vortex pairs generated by the ejector of the presentinvention are paired and spaced so that the pressure differentials theycreate causes them to hug a downstream wall surface. FIG. 2C is atransverse cross-sectional view of a vortex pair which creates apressure differential that drives the vortex pair in a direction towardsthe downstream, inverted wall, thereby causing the vortex pair to hugthe downstream, inverted wall. Note that the inverted, downstream wallsurface shown in 2(c) has been drawn as having the same orientation asthe wall in FIG. 2B. If FIG. 2C were rotated 180 degrees so that thewall surface is, in fact, inverted, one can see that the situation isequivalent to the wall in FIG. 2B being above the vortex pair. Becausethe vortices of such a pair hug the downstream wall, they help maintainthe ejectant (with or without additive) that has been ejected by theejector into in the near-wall region, and thereby reduce the occurrenceof bursts and sweeps. Hereinafter, the ejector used with the method ofthe present invention will be called a “vortex duct” ejector because ofits innovative use of vortex structures to control polymermixture/solution dissipation.

[0021]FIG. 3 illustrates a vortex duct ejector that may be used inpracticing the method of the present invention. Additivemixture/solution 9 flows into the ejector from the left, moving towardslot I. In this embodiment, the boundary layer to be injected withadditive mixture/solution envelops the vortex duct ejector and the flowis from right to left, just as if the ejector were on a body moving tothe right in a stationary medium. Additive mixture/solution is ejectedfrom the slots II, III, and IV into the boundary layer of the ejectorbody. Optimal solution concentrations and volume flow rates aredetermined as required for each application.

[0022] Additive mixture/solution flowing into the ejector from the leftis directed toward slot I by diffuser 10 and cone 12. Interactionbetween one or more vanes (not labeled) attached to the framework 14reduces the irregularity of the flow. As the flow passes through slot I,dimples in cone 12 and longitudinal slots in diffuser 10 createquasi-longitudinal vortices.

[0023]FIG. 4 is a cross-sectional view of the cone 12, illustrating thedimples 15 in cone 12. FIG. 5 is a cross-sectional view of the diffuser10, illustrating the longitudinal slots 17 in diffuser 10. Interactionof vortices created by the dimples 15 and slots 17 promotes furtherunwinding, aligning, and stretching of the polymer molecules in themixture I solution. The width of slot I can be adjusted, or varied, bysliding the central tube 18 with attached cone 12 longitudinally. Thematerials and features of the diffuser 10 and cone 12 can also bechanged or modified to alter the vortical structures. The throttled andconditioned flow then passes out of slot I and through a system ofpassageways in framework 20. The size of the passageways in framework 20governs the shape of the dimples on cone 12 according to Condition (1):

0.25 d _(passaagways2O)≦d _(dimples12)≦0.5 d _(passageways20)  . . .Condition (1)

[0024] where d _(passageways20) is the diameter of the passageways inframework 20 and d _(dimples12) is the diameter of the dimples in cone12. The depth (h) of the dimples is given by Equation (1):

h _(dimples12)=0.25 d _(dimples12)  . . . Equation (1)

[0025] where h _(dimples12) is the depth of the dimples in cone 12, andd _(dimples12) is as defined above.

[0026] In addition, the grooves in diffuser 10 are defined by Equations(2) and (3):

B_(grooves10=) d _(dimples12)  . . . Equation (2)

W_(grooves10=) h _(grooves10)=0.25d _(dimples12)  . . . Equation (3)

[0027] where

[0028] B_(grooves10) is the center-to-center distance between thegrooves in the diffuser 10,

[0029] W_(grooves10) is the width of each groove in diffuser 10, and

[0030] h_(grooves10) is the depth of each groove in diffuser 10.

[0031] Vortex formation can be enhanced by fabricating the cone (12)from an elastomeric material with characteristics what satisfy theequation

(E/ρ)^(½)=0.5 U∞  . . . Equation (4)

[0032] where E is the modulus of elasticity, ρ is the density, and U∞ isthe velocity of the exterior flow. For additional vortex enhancement,one may use anisotropic elastomeric material characterized as follows

2≦E_(long)/E_(xverse)≦5  . . . Condition (2)

[0033] where E_(long) is the longitudinal modulus of elasticity andE_(xverse) is the transverse modulus of elasticity.

[0034] The system of passageways in framework 20 can be divided intofour groups. The first group 22 passes solution in the longitudinaldirection through a second set of passageways 24 in the fairing 26having a diameter one-half that of the dimples in cone 12 and out intothe flow path through slot II. Slot II is the laminar region ejector,and it is intended to thicken and condition the boundary layer upstreamof the slots III and IV. The concave shape of the upstream surface ofthe under-slot-chamber formed by stopper 28 creates longitudinal Görtlervortices and the shape formed by fairing 26 (FIG. 3) provides a convexCoanda surface. The surfaces of slot II are parallel at the aperture. Asthe flow from slot II enters the boundary layer, it is characterized bylongitudinal Görtler vortex structures immediately adjacent an attachedflow coming off the downstream convex Coanda surface. These longitudinalGörtler vortices condition the flow upstream of slot III. Slot II'scontribution to thickening and conditioning the boundary layer reducesdisturbances caused by the ejected flow at slots III and IV.

[0035] Another group of passageways 30 passes the mixture/solutionobliquely through the framework 20, the fairing 26, and rings 32, 34, 36and 38 to exit from slot III. The curvature of the upstream surface ofthe chamber under slot III is concave in order to produce a system oflongitudinal Görtler vortices, and these vortices are then amplified bydimples 33 on an elastic downstream surface of ejector ring 32. FIG. 6illustrates, in cross-sectional view, a portion of such an ejector ring32. The dimensions and pitch of the dimples in ring 32 are given by:

λ_(dimples32)=d_(dimples32)=((7.19×10⁵)/Re_(x))+(3.56×10⁻⁵)(Re_(x))+1.71  . . .Equation (5)

[0036] and

h _(dimples32)≦0.5 d _(dimples32)   . . . Equation (6)

[0037] where λ_(dimples32), d _(dimples32) and h _(dimples32) are thepitch, diameter and depth, respectively, in wall units y*, of thedimples 33 in ring 32, and Rex is the Reynolds number of the water flowimmediately downstream of slot IV. As is well known in the art, wallunits are a non-dimensional measurement of distance from a wall. Theycan be expressed as a length dimension using the following equation.

y=(y* v)/μ  . . . Equation (7)

[0038] where y is a dimensioned length, v is the kinematic viscosity ofthe fluid and μ is the friction velocity of the fluid.

[0039] Fabricating ring 32 from elastomeric material can further enhancethe Görtler vortices forming in the chamber under slot III. If anelastic material is chosen, its characteristics should satisfy Equation(4), above. For additional enhancement effects, one may use anisotropicelastomeric material characterized by Condition (2), above.

[0040] When ring 32 is located in a more upstream position than thatillustrated in FIG. 3, such that its transverse groove is locatedbeneath the edge of ring 36, the transverse groove 40 creates astationary transverse vortex within transverse groove 40. The lowpressure created by this transverse vortex draws the flow ejected fromslot III, including the longitudinal Görtler vortices, against the walland stabilizes the flow ejected from slot III. When ring 32 is locatedfarther from ring 36, the transverse groove generates a series oftransverse vortex rings, which escape and migrate downstream with theflow. The frequency at which these transverse vortices are released canbe controlled by periodic motion of rings 32 and 34 (i.e., byoscillating central rod 48 which indirectly supports ring 34 via frame14), or by changing the elastic characteristics of the ring 32 material.The dimensions of the transverse groove are given by:

w_(xverse40)=h _(xverse40)=0.5 d _(dimples32)  . . . Equation (8)

[0041] where w_(xverse40) is the width and h_(xverse40) is the depth,respectively, of the transverse groove 40.

[0042] The last group of passageways 42 in framework 20 passes theadditive mixture/solution obliquely into the space between adjustablerings 32, 34, 44 and 46 and out into the flow stream through slot IV. Aswith slot III, the curvature of the upstream surface of the chamberunder slot IV creates a system of longitudinal Görtler vortices that areamplified by the dimples in rings 44 and 46. These Görtler vorticesinteract with the vortices coming from slot III to form longitudinalwaveguides that act to retain the polymer solution near the wall. Thedimensions and spacing of the dimples in rings 44 and 46 are governed bythe same equations as the dimples in rings 32 and 34.

[0043] The width of slots I, III and IV can be either adjusted oroscillated by sliding cone 12 and/or the rings 32 and 34 longitudinally.Cone 12 is articulated on the end of tube 18, and rings 32 and 34 arearticulated by the central rod 48 via fasteners to frame 14. Byadjusting the slot widths, one can vary the ejection velocity of theadditive mixture/solution. The most effective drag reduction usuallyoccurs when the ejection velocity is in a range between 5% and 10% ofthe free stream velocity, The ejector body 50 and slot widths should beadjusted to provide an additive mixture/solution flow velocity in thisrange for the desired mixture/solution flow rate. An entirely differentslot structure can be achieved by removing rings 32 and 34 and replacingrings 44 and 46 with rings featuring longitudinal slots 52. Thelongitudinal slots 52 are positioned at an approximate multiple of thespacing of the naturally occurring quasi-longitudinal vortex pairs andcreate high-powered longitudinal vortices.

[0044] Of course, the ejector used to of the present invention need notbe limited to the embodiment specifically illustrated. Indeed numerousvariations of the ducted vortex ejector are possible. For example, rings32, 34, 44 and 46 may be replaced with rings having different materialand structural characteristics. Rather the scope of the invention shallbe defined as set forth in the following claims and their legalequivalents. Various modifications will occur to those skilled in theart as a result of reading the above description, and all suchmodifications as would be obvious to one ordinary skill in the art areintended to be within the spirit of the invention disclosed.

What is claimed is:
 1. A method of reducing the dissipation rate of asecond fluid ejected into the boundary layer of a first fluid flowingrelative to a first surface, said method comprising the following steps:(a) forming pairs of Görtler vortices, using an upstream concave surfacethat forms a chamber under the first surface, wherein the vortices areshed, ejected, and flow downstream along the first surface; (b)releasing the second fluid into a region consisting substantially ofonly the near-wall region of a boundary layer of the first fluid bycausing the second fluid to flow over a convex Coanda surface as itenters the flow path of the first fluid, said convex Coanda surfacebeing located on the downstream side of a slot through which the secondfluid enters the flow path; and (c) controlling the ejection velocity ofthe second fluid such that the convex Coanda surface directs the flow ofthe second fluid into the first fluid so that the flow lines of secondfluid are substantially parallel to the flow lines of the first fluid.2. The method of claim 1, and further including: prior to release of thesecond fluid into the first fluid, adding a drag-reducing additive tothe second fluid.
 3. The method of claim 2, and further including, priorto release of the second fluid containing a drag-reducing additive,conditioning the drag-reducing additive by using fluid shear forces tocause the second fluid to flow between surfaces having conditioningmeans to thereby cause any high molecular weight, drag-reducingmolecules in said second fluid to be in immediate condition for reducingdrag.
 4. The method of claim 1, and further comprising: heating thesecond fluid prior to release of the second fluid into the first fluid.5. The method of claim 2, and further including heating the second fluidprior to release of the second fluid into the first fluid.
 6. The methodof claim 1, wherein the primary constituent of the first fluid is ahydrocarbon.
 7. The method of claim 1, wherein the primary constituentof the second fluid is the same as the primary constituent of said firstfluid.
 8. The method of claim 1, wherein the primary constituent of thefirst fluid and the primary constituent of the second fluid is water. 9.The method of claim 2, and further including the step of extending thetime the drag-reducing substance remains in the near-wall region bycreating a stationary transverse vortex using a transverse groovedownstream from the convex Coanda surface.
 10. The method of claim 1,and further including using an elastomeric material downstream from theconvex Coanda surface in order to enhance the Görtler vortices.
 11. Themethod of claim 8, wherein the elastomeric material includes dimples inorder to amplify the Görtler vortices.
 12. A method of causing adrag-reducing substance that is released into the boundary layer of afluid flowing relative to a first surface to remain in the immediatevicinity of said first surface, said method comprising the followingstep: causing fluid to flow over a concave surface located on anupstream wall of a slot ejector which releases the drag-reducingsubstance into said first fluid, said slot ejector including across-sectional area that temporarily increases in the region of theconcave surface so as to allow paired Görtler vortices to form and flowdownstream, said Görtler vortices having rotations, relative to thefirst surface, that are opposite to the rotational directions ofnaturally-occurring Görtler vortex pairs formed by the first surface,whereby lower pressure regions are produced in the boundary layer so asto cause the released drag-reducing substance to remain in the vicinityimmediately adjacent said first surface while said vortices areoperative.
 13. An apparatus which ejects a second fluid into a boundarylayer region of a first fluid flowing along a wall, said apparatuscomprising: a first slot ejector for ejecting the second fluid, saidfirst slot ejector having, on the upstream side of the first slotejector, a concave surface which forms a portion of a chamber in whichGörtler vortices may form; a convex Coanda surface on the downstreamside of the first slot ejector, said convex Coanda surface exhibitingthe Coanda effect, that is, causing adherence along the convex Coandasurface in the flow direction of the second fluid ejected from the firstslot ejector so that the flow lines of the ejected second fluid aresubstantially aligned with the direction of flow of the first fluidalong said wall.
 14. The apparatus of claim 10, and further comprising:a second slot ejector in the wall, said second slot ejector locatedalong the wall downstream from the first slot ejector, said second slotejector including a concave surface on the upstream side and a Coandasurface on the downstream side of the second slot ejector, said secondslot ejector including dimples or grooves on the Coanda surface.
 15. Theapparatus of claim 10, and further comprising a third slot ejectorlocated upstream from said first slot ejector, said third slot ejectorincluding a concave surface on an upstream side and a Coanda surface onthe downstream side, respectively.
 16. The apparatus of claim 10, andfurther comprising a transverse groove located downstream from saidfirst slot ejector, said transverse groove for creating a stationarytransverse vortex of fluid within the transverse groove due to flowalong the wall.
 17. The apparatus of claim 10, and further comprising asolid material having a transverse groove downstream from said firstslot, the solid material or position thereof can be varied so as to formeither a stationary transverse vortex within the transverse groovedownstream from said first slot, or a series of transverse vortex ringsdownstream from said first slot which escape and migrate downstream withthe flow.
 18. The apparatus of claim 15, and further including means tocontrol the frequency at which the series of transverse vortex rings arereleased.
 19. The apparatus of claim 10, and further including dimplesor grooves on the convex Coanda surface.
 20. The apparatus of claim 10,and further including dimples or grooves on a surface downstream of saidconvex Coanda surface.
 21. The apparatus of claim 10, and furthercomprising: a surface, downstream of the first slot ejector, havingdimples or grooves therein to amplify Görtler vortices produced by thefirst slot ejector; and a transverse groove, downstream of the firstslot ejector, which draws the ejected fluid with Görtler vorticestherein against the wall.
 22. The apparatus of claim 10, and furtherincluding dimples on the convex Coanda surface, said dimples having apitch defined by the following equation:λ_(dimples32)=((7.19×10⁵)/Re_(x))+(3.56×10−5)(Re_(x))+1.71 whereλ_(dimples32) is the pitch, in wall units y*, of the dimples, and Re_(x)is the Reynolds number of the fluid flowing along the convex Coandasurface.
 23. The apparatus of claim 10, and further including dimples onthe convex Coanda surface, said dimples having a diameter defined by thefollowing equation:d_(dimples32)=((7.19×10⁵)/Re_(x))+(3.56×10⁻⁵)(Re_(x))+1.71 whered_(dimples32) is the diameter, in wall units y*, of the dimples, andRe_(x) is the Reynolds number of the fluid flowing along the convexCoanda surface.
 24. The apparatus of claim 21, said dimples having adepth that is defined by the following equation: h_(dimples32≦)0.5d_(dimples32) where h_(dimples32) is the depth of the dimples.